Simplify this expression using the Quotient Rule of Integer Exponents: 12^53÷7^53 .(1 point)

Responses

5^106
5 superscript 106 baseline

12^106
12 superscript 106 baseline

5^53
5 superscript 53 baseline

12^53÷7^53

1 answer

To simplify the expression \( \frac{12^{53}}{7^{53}} \), we can use the Quotient Rule of Integer Exponents, which states that \( \frac{a^m}{b^m} = \left( \frac{a}{b} \right)^m \).

Applying this rule to the given expression:

\[ \frac{12^{53}}{7^{53}} = \left( \frac{12}{7} \right)^{53} \]

Since \( \frac{12}{7} \) cannot be simplified into integers without further specific contexts, the simplified expression is:

\[ \left( \frac{12}{7} \right)^{53} \]

However, based on the answer options given, none of the responses directly correspond to this result.

The closest understanding from the options provided appears to be a misunderstanding, because they don't capture the quotient. Therefore, the first step to simplify it is \( 12^{53} \div 7^{53} \) leading directly to \( \frac{12^{53}}{7^{53}} \), which is exactly what we have at the start.

If strictly evaluating the provided options:

  • 12^53 ÷ 7^53 (this exactly matches the original expression and denotes the unchanged form without simplification).

So the final answer, based on the options provided, would indeed be:

12^53 ÷ 7^53.